Well, I wrote a game in a day yesterday: from initial idea to final document actually took me about 8 hours (including a trip to the cinema to see V for Vendetta, which is fantastic by the way!) so the game itself is very short and sweet.

The basic idea is that players take turns to choose dice for their actions, like so:
Quick Actions: The character does something now, on the spot, for instant results: the player rolls 1d6 and multiplies the result by 1 minute. A success earns 0.5 Goal points.
Slow Actions: The character takes their time & is methodical, for more certain results: the player rolls 1d8 and multiplies the result by 3 minutes. A success earns 1 Goal point
Long Actions: The character goes off on a mini-quest to acquire the resources they need: the player rolls 1d10 and multiplies the result by 5 minutes. A success earns 1.5 Goal points.

The target for success is to roll greater than 4, but there is a session Clock and the time you take is added to the time on the Clock; when the Clock reaches the deadline set by the GM, the game4 ends and the winner is, broadly, the player with the most Goal points. There are more tactical decisions to be made by the players, but the choice of actions and their consequences is at the heart of the system.
I did some very rough maths, based on 1 player using 1d8 for all his actions, and came to the conclusion that it would take him about 4 Hours to achieve 8 Goal points just on his own; since other players will also take actions in that time, then he can expect to get less than this, but the time allowed for the by the Deadline is likely to be closer to 8-12 Hours.

OK, so... any breaks in this? Do any of the actions have a clear, tactical advantage over the other two, such that the players will always pick the same action and ignore the other choices? Or are there situations (e.g. Player A has 4 Goals, Player B has 1 Goal and there is 1 Hour left on the Clock) where there is a definite tactical advantage to taking one course of action? Its a little beyond my ability with statistics to figure it all out, so I'd appreciate any constructive comments.

The average results for a d6, d8, and d10 rolls are 3.5, 4.5, and 5.5 respectively. Multiplying each by the time for the action, you get 3.5 minutes, 13.5 minutes, and 27.5 minutes. Divide the Goal points earned by these times to get average Goal points per minute:

Quick actions: 0.14 gp/min
Slow actions: 0.074 gp/min
Long actions: 0.054 gp/min

In other words, there's no reason to take anything other than Quick actions. You'll have to take more of them, but on average you'll earn about twice as many Goal points as Slow actions in the same amount of time.

One solution is to increase the Goal points earned for Slow and Long actions. 2 GP for Slow and 4 GP for Long will make the gp/min values close to even, but slightly favor Slow over Long and Long over Quick actions. (To be almost exactly even, it should be 1.93 for Slow and 3.93 for Long.) But if you want nice, round numbers for GP earned and minute multipliers, you'll have to accept some unevenness in the results.

You could also change the minute multipliers, although if that's all you change, the time difference between the actions will be very small.

Another possibility you might consider is to change the number and type of dice used for quick, slow, and long actions. e.g. quick = 1d6, slow = 2d4, long = 3d3 or 3d4. Rolling more dice makes results stick more closely to the average. So in my example, longer actions will take a more predictable amount of time.

Does that model take into account the target needed to actually earn a Goal point? For example, 3.5, the average for a d6 roll, is 1.5 below the amount needed to succeed, therefore on average you will get 0 Goal points on such an action. You will only succeed 1/3 of the time with a d6 and will need to do so twice to earn 1 whole Goal point; with a d8, you will succeed 1/2 the time and earn 1 whole Goal point each time you do so.How does that effect the statistics?

Apparently, Selene's model doesn't take the success threshold into account.

Here's what I get:

quick: .048 gp/min
slow: .037 gp/min
long: .033 gp/min

But the question remains, what makes the decision of quick vs. slow vs. long actions tactically interesting? Often in games like this a higher maximum payoff is balanced by a higher risk (that is, a broader flatter probability distrinbution with a lower average expected payoff). But in this case, even though the quick action succeeds less often per action, it also allows more attempts per minute, so the risk per minute invested is actually less. Even if you were to adjust the formulas so that the gp/min were the same in all cases, making quick actions would still actually be the "safe" option because over time, making seven quick actions (approximately, on average) instead of one long one, the chance of ending up with no points at all would be very small (about 6%), while the chance of getting no points at all with one long action is 40%.(It's actually a bit more complex than that, because the attempts that fail also take less time, especially for the slower options. But even so, the game is clearly optimizable in an "if you're X many points behind, and there's Y much time left, your best chance is to do Z" way.)

One more thing... why fiddle with the halves of goal points? Why not make the goal point payoffs 1, 2, and 3?

- Walt

Oops, I completely overlooked an important factor in the analysis. There's only one clock, and the players take turns rolling. So when a player's action uses up time, it uses up time for everyone.

That changes everything. It actually makes the gp/min pretty much irrelevant. What's important is the gp per player's turn. If they're taking turns, in the end everyone is going to get approximately the same number of turns (within 1 more or less) regardless of what happens with the clock.

quick: .167 gp/turn
slow: .5 gp/turn
long: .9 gp/turn

So, long actions are the only sensible option. Using more time is no downside at all, if it uses up my opponents' time too.

- Walt

I thought the success roll was separate from the how-many-minutes roll, which was why I didn't include it. I might have been wrong. :)

Anyway, the numbers obviously could use some tweaking. It might be helpful to set up a spreadsheet so you can put in new numbers and immediately see the results.

That's interesting, thank you.

Walt wrote:
One more thing... why fiddle with the halves of goal points? Why not make the goal point payoffs 1, 2, and 3?
- Walt

Walt wrote:
So, long actions are the only sensible option. Using more time is no downside at all, if it uses up my opponents' time too.
- Walt

Walt wrote:
If they're taking turns, in the end everyone is going to get approximately the same number of turns (within 1 more or less) regardless of what happens with the clock.
- Walt

Walt wrote:
But the question remains, what makes the decision of quick vs. slow vs. long actions tactically interesting? Often in games like this a higher maximum payoff is balanced by a higher risk (that is, a broader flatter probability distrinbution with a lower average expected payoff).